By definition, Bronsted-Lowry acid is a proton donor in the acid-base neutralization reaction. When a weak acid like acetylsalicylic acid is reacted with water, the water here acts as the Bronsted-Lowry base. This is possible because water has properties of amphoterism - can act as an acid or base. In this case, acetylsalicylic acid would have to donate its H+ atom to water, so that it would yield a hydronium ion, H₃O⁺. The complete net ionic reaction is shown in the picture.
So, in the reaction, the products yield are the acetylsalicylate ion and the hydronium ion.